Utility proportional beliefs

Bach, Christian W.; Perea, Andrés

doi:10.1007/s00182-013-0409-3

Cited by 7 publications

(6 citation statements)

References 15 publications

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“…The performance was slightly improved by comparing the belief probabilities predicted by UPB to the observed actions, but even then the performance was still the worst of the various equilibrium concepts. Our interpretation of the UPB solution is consistent with the presentation in Bach and Perea (2014), but there may be alternative interpretations which would provide a better fit to the data.…”

Section: Discussionsupporting

confidence: 82%

“…Players are then assumed to take actions which maximise their expected utilities given their belief probabilities, so in the UPB model beliefs and actions do not coincide. Bach and Perea (2014) show that there is a unique UPB solution in two player games which is obtained by iteratively eliminating utility-disproportional beliefs. They also discuss 'level-k' solutions in which the elimination of utility-disproportional beliefs is done only k times, for which the final solution is not guaranteed to be a singleton.…”

Section: Discussionmentioning

confidence: 99%

“…The paper by McKelvey and Palfry (1995, p. 31) introducing the QRE discusses the 9 We note that in the QRE the range of the error parameter is therefore i P i ∈ [−∞, ∞] and therefore it allows for the possibility of negative estimated payoffs. In the BRNE/RBB (1 + i ) ∈ [0, ∞] and so negative estimated payoffs only arise for P i < 0.…”

Section: Probabilistic Actionsmentioning

confidence: 99%

“…The Utility Proportional Beliefs (UPBs) model introduced by Bach and Perea (2014) shares the notion of uncertain rather than random beliefs. In that model, beliefs are assigned in proportion to expected payoffs.…”

Section: Probabilistic Beliefsmentioning

confidence: 99%

“…We choose these two models as the primary focus of comparison for our study because they can be derived from a set of behavioral axioms. We then compare and contrast them to other probabilistic choice models of decision making in game theory such as the Quantal Response Equilibrium (QRE) model proposed by McKelvey and Palfrey (1995), the Boundedly Rational Nash Equilibrium (BRNE) model of Chen, Friedman and Thisse (1997), the Random Belief Equilibrium (RBE) proposed by Friedman and Mezzetti (2005) and the Utility Proportional Beliefs (UPB) model proposed by Bach and Perea (2014). Blavatskyy (2011) showed that their model fitted experimental data better than other existing probabilistic models.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic-choice models

Limited-Dependent and Qualitative Variables in Econometrics

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We examine a number of probabilistic choice models in which people might form their beliefs to play their strategies in a game theoretic setting in order to propose alternative equilibrium concepts to the Nash equilibrium. In particular, we evaluate the Blavatskyy model, Returns Based Beliefs (RBB) model, Quantal Response Equilibrium (QRE) model, Boundedly Rational Nash Equilibrium (BRNE) model and the Utility Proportional Beliefs (UPB) model. We outline the foundational axioms for these models and fully explicate them in terms of probabilistic actions, probabilistic beliefs and their epistemic characterizations. We test the model predictions using empirical data and show which models perform better under which conditions. We also extend the Blavatskyy model which was developed to consider games with two actions to cases where there are three or more actions. We provide a nuanced understanding of how different types of probabilistic choice models might predict better than others.

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Section: Discussionsupporting

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Probabilistic Actionsmentioning

confidence: 99%

Section: Probabilistic Beliefsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic-choice models

Limited-Dependent and Qualitative Variables in Econometrics

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Rational Coordination Without Beliefs

Colombo

Guala

2021

Erkenn

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Bounded rationality for relaxing best response and mutual consistency: the quantal hierarchy model of decision making

Evans

Prokopenko

2023

Theory Decis

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While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still approximating level-k, QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling.

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Utility proportional beliefs

Cited by 7 publications

References 15 publications

Probabilistic-choice models

Probabilistic-choice models

Rational Coordination Without Beliefs

Bounded rationality for relaxing best response and mutual consistency: the quantal hierarchy model of decision making

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